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Simplifying x2 + 0.012x + -0.0039 = 0 Reorder the terms: -0.0039 + 0.012x + x2 = 0 Solving -0.0039 + 0.012x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.0039' to each side of the equation. -0.0039 + 0.012x + 0.0039 + x2 = 0 + 0.0039 Reorder the terms: -0.0039 + 0.0039 + 0.012x + x2 = 0 + 0.0039 Combine like terms: -0.0039 + 0.0039 = 0.0000 0.0000 + 0.012x + x2 = 0 + 0.0039 0.012x + x2 = 0 + 0.0039 Combine like terms: 0 + 0.0039 = 0.0039 0.012x + x2 = 0.0039 The x term is 0.012x. Take half its coefficient (0.006). Square it (0.000036) and add it to both sides. Add '0.000036' to each side of the equation. 0.012x + 0.000036 + x2 = 0.0039 + 0.000036 Reorder the terms: 0.000036 + 0.012x + x2 = 0.0039 + 0.000036 Combine like terms: 0.0039 + 0.000036 = 0.003936 0.000036 + 0.012x + x2 = 0.003936 Factor a perfect square on the left side: (x + 0.006)(x + 0.006) = 0.003936 Calculate the square root of the right side: 0.062737549 Break this problem into two subproblems by setting (x + 0.006) equal to 0.062737549 and -0.062737549.Subproblem 1
x + 0.006 = 0.062737549 Simplifying x + 0.006 = 0.062737549 Reorder the terms: 0.006 + x = 0.062737549 Solving 0.006 + x = 0.062737549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.006' to each side of the equation. 0.006 + -0.006 + x = 0.062737549 + -0.006 Combine like terms: 0.006 + -0.006 = 0.000 0.000 + x = 0.062737549 + -0.006 x = 0.062737549 + -0.006 Combine like terms: 0.062737549 + -0.006 = 0.056737549 x = 0.056737549 Simplifying x = 0.056737549Subproblem 2
x + 0.006 = -0.062737549 Simplifying x + 0.006 = -0.062737549 Reorder the terms: 0.006 + x = -0.062737549 Solving 0.006 + x = -0.062737549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.006' to each side of the equation. 0.006 + -0.006 + x = -0.062737549 + -0.006 Combine like terms: 0.006 + -0.006 = 0.000 0.000 + x = -0.062737549 + -0.006 x = -0.062737549 + -0.006 Combine like terms: -0.062737549 + -0.006 = -0.068737549 x = -0.068737549 Simplifying x = -0.068737549Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.056737549, -0.068737549}
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